The estimation procedure of Paulson, Holcomb and Leitch (1975) for the parameters of the stable laws is shown to be similar in spirit to the modified X2minimum procedure. This observation suggests that a class of modified integrated squared error procedures may be developed for the stable laws as well as much more generally. For the stable case, some influence curves, asymptotic covariances, and efficiencies are given, and the robustness of maximum likelihood estimators is discussed.